One law for all gases
At ordinary temperatures and pressures, most gases behave in the same simple way: their pressure, volume, amount and temperature are tied together by the ideal gas law, PV = nRT. Know three of them and you can find the fourth. It works for air in a tire, helium in a balloon or carbon dioxide in a soda bottle.
The formula
- PV = nRT
- P: pressure, V: volume, n: amount in moles, T: absolute temperature in kelvin
- R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K)
- T (K) = T (°C) + 273.15
- Mass of gas = n × molar mass; density ρ = P × M ÷ (R × T)
The calculator converts atm, kPa, bar, psi, mmHg, liters, milliliters and cubic feet for you.
Worked example: molar volume
What volume does 1 mole of gas take at 0 °C and 1 atm?
- T = 0 + 273.15 = 273.15 K.
- V = nRT ÷ P = 1 × 0.08206 × 273.15 ÷ 1 = 22.41 L.
- For air (28.97 g/mol), that volume weighs 28.97 g, a density of 1.29 kg/m³.
At 20 °C the same mole takes 24.05 L, and at body temperature (37 °C) about 25.4 L.
Worked example: a helium balloon
A party balloon holds about 10 L of helium at 20 °C and 1 atm.
- n = PV ÷ RT = 1 × 10 ÷ (0.08206 × 293.15) = 0.416 mol.
- Mass of helium: 0.416 × 4.0026 = 1.66 g.
- The same volume of air weighs about 12 g, so the balloon can lift roughly 10 g, minus the weight of the rubber.
Related gas laws
| Law | Held constant | Relationship |
|---|---|---|
| Boyle’s law | n, T | P1V1 = P2V2 |
| Charles’s law | n, P | V1 ÷ T1 = V2 ÷ T2 |
| Gay-Lussac’s law | n, V | P1 ÷ T1 = P2 ÷ T2 |
| Avogadro’s law | P, T | V ÷ n is constant |
Each is a special case of PV = nRT.
When the law breaks down
- High pressure: above about 10 atm, the volume of the molecules themselves and their attractions matter. A scuba tank at 200 atm holds a few percent less air than the ideal law predicts.
- Low temperature: near the boiling point, gases condense and stop behaving ideally.
- Steam and polar gases such as ammonia deviate more than helium or nitrogen.
For those cases, chemists use real-gas equations such as van der Waals.
Common mistakes
- Using °C or °F directly: always convert to kelvin.
- Mixing units for R: use 0.08206 with liters and atm, 8.314 with cubic meters and pascals.
- Forgetting that gauge pressure (tire gauges) excludes the 14.7 psi of the atmosphere: add it to get absolute pressure.